The Market is the first money-boosting building, significantly increasing a city's output of gold. It usually becomes available at a moment in the civilization's development when it's short on gold (you've accumulated buildings and units, you're starting to build your road system, but aren't trading with other civilizations much yet) so it is important to research Currency and start building it in your cities to overcome the shortage.

Build it first in cities with good Gold output - this way the 25% boost will have greater effect earlier on.

It also allows the creation of one Merchant specialist, increasing the speed at which Great Merchants appear.

In Brave New World the Market's general purpose changes a bit, becoming a booster for international trade. The Market becomes more effective as the number of Trade Routes passing through a city increases, so when prioritizing where to build it first, check and see which of your cities have the most Trade Routes with other civilizations.

A market is a location where farmers and tradesmen and merchants bring their wares to sell. While the earliest and most primitive markets may have operated under a barter system, a truly successful market requires a working trusted currency to allow for the free exchange of goods and services. For obvious reasons, markets are located where the customers are, in villages, towns and cities. Smithfield has been a meat-trading market in London for over a thousand years, which helps to explain some of the street names like, "Cow Cross Street."